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In this paper, we investigate infinite horizon jump-diffusionforward-backward stochastic differential equations under some monotonicityconditions. We establish an existence and uniqueness theorem, two stabilityresults and a comparison theorem for solutions to such kind of equations. Thenthe theoretical results are applied to study a kind of infinite horizonbackward stochastic linear-quadratic optimal control problems, and thendifferential game problems. The unique optimal controls for the controlproblems and the unique Nash equilibrium points for the game problems areobtained in closed forms.

Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems